Abstract
Using the language of pseudospectra, we study the behavior of matrix eigenvalues under two scales of matrix perturbation. First, we relate Lidskii’s analysis of small perturbations to a recent result of Karow on the growth rate of pseudospectra. Then, considering larger perturbations, we follow recent work of Alam and Bora in characterizing the distance from a given matrix to the set of matrices with multiple eigenvalues in terms of the number of connected components of pseudospectra.
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J. V. Burke’s research was supported in part by National Science Foundation Grant DMS-0505712.
A. S. Lewis’s research was supported in part by National Science Foundation Grant DMS-0504032.
M. L. Overton’s research was supported in part by National Science Foundation Grant DMS-0412049.
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Burke, J.V., Lewis, A.S. & Overton, M.L. Spectral conditioning and pseudospectral growth. Numer. Math. 107, 27–37 (2007). https://doi.org/10.1007/s00211-007-0080-3
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DOI: https://doi.org/10.1007/s00211-007-0080-3